Difference between revisions of "Manuals/calci/SKEW"

Latest revision as of 13:40, 18 June 2018

SKEW()

Parameters are any numbers to calculate the skewness.
- SKEW() returns the skewness of a distribution

Description

This function gives the Skewness of a distribution.
Skewness is a measure of the degree of asymmetry of a distribution.
A distribution(normal distribution) is symmetry ,it don't have a Skewness.
In a distribution the left tail is more pronounced than the right tail (towards more negative values) then the function is said to have Negative Skewness.
If a distribution is skewed to the right, the tail on the curve's right-hand side is longer than the tail on the left-hand side (towards more positive values), then the function is said to have a positive skewness.
In a Left Skewed Distribution, its $mean<median<mode$
In a Normal Skewed Distribution, its $mean=median=mode$
In a Right Skewed Distribution, its $mode<median<mean$ .
In $SKEW(),Firstparameterisrequired.Fromthesecondparameterareoptional.*Incalcithereisnorestrictionforgivingthenumberofarguments.*Theargumentscanbebeeithernumbersornames,array,constantsorreferencesthatcontainnumbers.*Supposethearraycontainstext,logiclvaluesoremptycells,likethatvaluesarenotconsidered.*TheequationforSkewnessisdefinedby:<math>Skewness={\frac {n}{(n-1)(n-2)}}\sum \left({\frac {x_{i}-{\bar {x}}}{s}}\right)^{3}$

Where, $s$ is the sample standard deviation, ${\bar {x}}$ represents a sample mean.

This function will return the result as error when

 1. Any one of the argument is non-numeric. 
 2. If there are fewer than three data points, or the Sample Standard Deviation is zero.

Examples

Spreadsheet
	A	B	C	D	E
1	0	4	-5	4	1
2	29	9	11	5	2
3	41	11	18	2	3
4	18	10	7	5	5
5	4	5	9	6	6
6	38	9	13	8	11

=SKEW(B1:B5) = -0.4369344921493
=SKEW(A1:A6) = -0.21921252920
=SKEW(C1:C4) = -0.715957010
=SKEW(D1:D6) = 0
=SKEW(E1:E6) = 1.16584702768

References

Skewness

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''SKEW(n1,n2,…)'''</div><br/>
+<div style="font-size:30px">'''SKEW()'''</div><br/>
-*<math>n_1,n_2,…</math> are numbers to calculate the skewness.
+*Parameters are any numbers to calculate the skewness.
+**SKEW() returns the skewness of a distribution
 ==Description==
-*This function gives the skewness of a distribution.
+*This function gives the Skewness of a distribution.
 *Skewness is a measure of the degree of asymmetry of a distribution.
-*A distribution(normal ditribution) is symmetry ,it don't have a skewness.
+*A distribution(normal distribution) is symmetry ,it don't have a Skewness.
-*In a  distribution  the left tail  is more pronounced than the right tail  (towards more negative values) then the function is said to have negative skewness.
+*In a  distribution  the left tail  is more pronounced than the right tail (towards more negative values) then the function is said to have Negative Skewness.
-*In a distribution is skewed to the right , the tail on the curve's right-hand side is longer than the tail on the left-hand side (towards more positive values), then the function is said to have a positive skewness.
+*If a distribution is skewed to the right, the tail on the curve's right-hand side is longer than the tail on the left-hand side (towards more positive values), then the function is said to have a positive skewness.
-*In a left skewed distribution ,its mean<median<mode.
+*In a Left Skewed Distribution, its <math>mean<median<mode</math>
-*In a normal  skewed distribution, its mean=median=mode.
+*In a Normal Skewed Distribution, its <math>mean=median=mode</math>
-*In a right skewed distribution, its mode<median<mean.
+*In a Right Skewed Distribution, its <math>mode<median<mean</math>.
-*In <math>SKEW(n_1,n_2,...), n_1</math>  is required.<math>n_2,n_3,...</math> are optional.
+*In <math>SKEW(), First parameter is required.From the second parameter are optional.
 *In calci there is no restriction for giving the number of arguments.
 *The arguments can be be either numbers or names, array,constants or references that contain numbers.
 *Suppose the array contains text,logicl values or empty cells, like that values are not considered.
-*The equation for skewness is defined by :<math> Skewness= \frac{3(mean-median)}{s}</math>  OR <math>skewness= \tfrac{\sum (x_i-\bar{x})^3}{(N-1)s^3}</math>  Where:  s is the sample standard deviation, <math>\bar{x}</math> represents a sample mean.
+*The equation for Skewness is defined by :<math> Skewness = \frac{n}{(n-1)(n-2)}\sum \left(\frac{x_i-\bar{x}}{s} \right)^3</math>
+Where, <math>s</math> is the sample standard deviation, <math>\bar{x}</math> represents a sample mean.
 *This function will return the result as error when
-. Any one of the argument is nonnumeric.
+. Any one of the argument is non-numeric.
-. If there are fewer than three data points, or the sample standard deviation is zero.
+. If there are fewer than three data points, or the Sample Standard Deviation is zero.
+==Examples==
+{| class="wikitable"
+|+Spreadsheet
+|-
+! !! A !! B !! C !! D!! E
+|-
+! 1
+| 0 || 4 || -5 ||4 || 1
+|-
+! 2
+| 29 || 9 || 11 || 5 || 2
+|-
+! 3
+| 41  || 11  || 18  ||2 || 3
+|-
+! 4
+| 18 ||10  || 7  ||5 ||5
+|-
+! 5
+| 4 || 5 || 9  ||6 || 6
+|-
+! 6
+| 38 || 9 || 13  || 8 || 11
+|}
-==Examples==
+*=SKEW(B1:B5) = -0.4369344921493
+*=SKEW(A1:A6) = -0.21921252920
+*=SKEW(C1:C4) = -0.715957010
+*=SKEW(D1:D6) = 0
+*=SKEW(E1:E6) = 1.16584702768
+==Related Videos==
+{{#ev:youtube|B0xF7UILeKo|280|center|SKEW}}
 ==See Also==
+*[[Manuals/calci/KURT| KURT]]
+*[[Manuals/calci/STDEV  | STDEV ]]
+*[[Manuals/calci/STDEVP | STDEVP ]]
 ==References==
+*[http://en.wikipedia.org/wiki/Skewness Skewness]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/SKEW"

Latest revision as of 13:40, 18 June 2018

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Description

Examples

Related Videos

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